The present invention relates to the cancellation of vibrations in devices such as machinery. Many machines or machine elements have a periodic disturbing force applied to them which excites vibrations therein. For example, the imbalance in the rotor of a rotating machine will cause a periodic disturbing force to be applied to the stator. The disturbing force is transmitted through the bearings at the frequency of revolution of the rotor. In fact, the disturbing force can be, and usually is, much more complicated. Typically, the disturbing force also excites vibrations in the stator at frequencies which are harmonics of the frequency of revolution of the rotor (the fundamental frequency). Another example of a device in which a periodic disturbing force excites vibrations is an electrical transformer caused to vibrate at the frequency of the alternating currents flowing therein and at harmonics thereof.
It has been known to attempt to cancel or compensate for the periodic disturbing force applied to a vibrating system in order to attenuate the vibrations therein. In the most simple of systems, a compensating force is applied between a reacting mass and the vibrating device. The theory can be explained with reference to FIG. 1., A periodic disturbing force F.sub.D (.omega.t) acts upon the vibrating mass M which is supported on an elastic foundation K. The vibrations or periodic movements of the vibrating mass M take place in the direction of the arrow X. If a force F.sub.2 (.omega.t) equal and opposite to the disturbing force acts between the vibrating mass M and an auxiliary reacting mass M.sub.2, the vibration of mass M can be attenuated. Of course, the reacting mass will have a reciprocating motion X.sub.2. One method of creating the compensating force F.sub.2 (.omega.t) is with an electromagnet actuator placed between masses M and M.sub.2. FIG. 2 schematically illustrates the use of auxiliary reacting masses M.sub.R positioned between electromagnets 10 in the stator 11 of a rotating machine for cancellation of vibrations caused by disturbing forces transmitted to the stator from the rotor 12 through the bearings 13, 14.
It is not necessary to use auxiliary reacting masses. The mass causing the disturbing force may itself be used as the reacting mass. This is especially the case where the rotor of a rotating machine is supported by active electromagnetic bearings. FIG. 3 illustrates a rotating machine having active magnetic bearings 15, 16. The rotor 12 is used as the reacting mass. This approach has the advantage of attacking the vibration at the source. In a variation of this scheme, the rotor is supported in its normal location by fluid bearings and the electromagnets are simply used to generate the compensating forces to attenuate the vibrations in the stator.
The compensating force (F.sub.2 (.omega.t) in FIG. 1) must be applied at the correct amplitude and phase if the vibrations in the vibrating mass are to be attenuated. If vibrating devices were perfectly rigid and perfect accelerometers and actuators existed with fixed gain and no phase delay, then finding the correct amplitude and phase for the signal applied to the actuator to generate the compensating force would be a simple matter--at least if only the fundamental frequency need be considered. The dynamics of the system which includes the actuator, the vibrating mass and the accelerometer are not so simple. For every system there exists a transfer function which defines the relation between the input signal to the actuator and the output signal of the accelerometer. The transfer function defines a unique gain (ratio of the amplitude of the input signal to the amplitude of the output signal) and phase shift (electrical degrees between the input signal and the output signal) for every frequency of the input signal. FIG. 4 is a graph of an input signal and an output signal for the purpose of illustrating gain and phase shift. FIG. 5 illustrates a hypothetical transfer function showing the relation of gain and phase delay versus frequency. The transfer function for a vibrating device would most certainly be more complicated. As a practical matter, the transfer function may be difficult to calculate from measured system parameters. In general, however, as frequency increases beyond a certain threshold, the output signal will lag the input signal, and beyond another threshold the amplitude of the output signal will decrease.
The manner in which the dynamics of the system complicate the generation of the compensating force becomes apparent when considering that a compensating force must be created for vibrations at the fundamental frequency and each harmonic. The gain and phase delay are different for each compensating signal applied to the actuator, and the transfer function cannot be defined by calculation. This problem, however, was solved by the adaptive vibration control circuit or adaptive controller.
An adaptive controller is described in Chaplin and Smith U.S. Pat. No. 4,490,841 entitled "Method and Apparatus for Cancelling Vibrations." The adaptive controller accepts as an input signal, a signal generated by an accelerometer which contains components at the fundamental frequency and all harmonics at which vibrations have been excited. A reference signal at the fundamental frequency of the disturbing force is also accepted by the adaptive controller. The adaptive controller first performs a Fourier Transform upon the accelerometer signal to identify the amplitude and phase of the spectral components of the signal corresponding to vibrations at the fundamental frequency and each harmonic (say the first four or five harmonics). For each spectral signal the adaptive controller modifies the amplitude and phase in an attempt to generate an input signal to the actuator (electromagnet generating the compensating force) that will attenuate the vibrations at that frequency. The modified spectral signals are combined by an inverse Fourier Transform and are applied as a drive signal to the actuator. By successive trial and error, the adaptive controller finds the correct modifications for each spectral component to reduce the vibrations corresponding to that frequency. The trial and error method applied separately to each spectral component eliminates any need for prior knowledge of the complex transfer function of the device. If only vibrations at the fundamental frequency are of concern, the adaptive controller can be greatly simplified. The Fourier Transform to identify spectral components can be eliminated.
FIG. 6 schematically illustrates the application of an adaptive controller to compensate for the horizontal vibrations transferred to a stator from a rotor journaled in a magnetic bearing. The magnetic bearing comprises four electromagnet poles 20, 21, 22, and 23 mounted in the stator (not shown) and spaced at 90 degrees to each other surrounding the rotor 12. The rotor has a ferrous (magnetic) outer ring in close proximity to the poles. The attractive force of each magnet is controlled by the currents Iy.sub.1, and Iy.sub.2 flowing in the magnet coils 24, 25. By carefully adjusting the currents in each magnet coil, the forces on the rotor can be brought into balance and, in theory, the rotor could stay at rest in a levitated state. However, this balanced condition represents an unstable equilibrium because the attractive forces of each electromagnet varies inversely with the distance between the pole and the rotor. Consequently, if the rotor moves an infinitesimal distance in any radial direction, the forces will become unbalanced. Thus, in order to maintain a stable state, it is necessary to use a feedback control circuit. The position of the rotor relative to the magnet poles is detected by position sensors. Only the position sensors 26, 27 and feedback control circuit for the vertical direction are shown in FIG. 6. Typical position sensors comprise inductive or eddy current type devices in combination with a high frequency source 28 of excitation and a demodulator 29 as schematically shown in the figure. The vertical shaft position (the "Y" position) is subtracted from a vertical reference signal at summing junction 30 to generate an error signal. The error signal drives the current applied to the magnet coils in the direction to reduce the error signal to near zero. The compensation block 31 in the forward path of the control circuit is a common device to overcome the problems introduced by the destabilizing inverse-force relationship in the electromagnets.
The adaptive controller 33 receives the acceleration signals from the accelerometers 34 (only one shown) mounted at the location where vibration is to be reduced. In this case the accelerometers are mounted to sense accelerations in the vertical direction. It also receives a speed signal which is representative of the frequency of rotation of the rotor (the fundamental frequency of the periodic disturbing force). The adaptive controller determines the amplitude and phase of the fundamental and each harmonic as high as, say, 600 Hertz. It then computes the cancellation wave shapes to inject into the magnetic bearing system (at summing junction 35) by a trial and error method to eliminate vibrations. Reductions on the order of 100 to 1 (40 dB) have been observed.
In a rotating machine wherein the rotor is suspended by two spaced radial bearings and one axial thrust bearing, there are five degrees of freedom addressed by the bearing system. Referring to FIG. 7, the degrees of freedom comprise perpendicular diametral displacements (X and Y displacements) at each radial bearing and an axial or Z displacement. Therefore, the magnetic bearing suspension system must comprise five independent position feedback control loops. The five degrees of freedom of the rotor 12 may be identified with five disturbing forces applied to the stator through the magnetic bearings each of which individually or in combination excite vibrations in the stator. To cancel all of the vibrations, accelerometers and adaptive controllers must be associated to some extent with each oppositely-positioned pair of electromagnets for each radial bearing. Such a system could effectively cancel the rigid body modes of vibration of the stator structure if the relationships between disturbing forces at the bearings and the vibrations sensed by the accelerometers at the bearings were substantially decoupled amongst the various axes of control. Unfortunately, in real life systems, there is a significant amount of cross-coupling amongst the axes of control. For example, a vibration-cancelling force introduced in the X.sub.1 axis may cause the vibration at X.sub.2, Y.sub.1, and Y.sub.2 to increase.
Cross-coupling can exist for many reasons, e.g., nonsymmetrical stator geometry relative to the rotor; center of gravity not on the axis of rotation; cantilevered support at the base; and nonsymmetrical stiffnesses in apparatus structure.
For example, in a rotating machine of the type being described with five degrees of freedom, there exists cross-coupling of forces applied to the rotor by each electromagnetic pole pair and the change in the gap of all pole pairs. This cross-coupling does not have a substantial effect on the bearing suspension system but is an impediment to the reduction of vibrations. The Chaplin and Smith patent discloses two approaches to multiple interacting systems. One involves an iterative process of considering one accelerometer actuator pair at a time. The other comprises premeasuring the cross-coupling coefficients between each actuator (electromagnet pair in the example of FIG. 6) and sensor and performing matrix operations to deduce the required cancellation signal on each cancelling actuator. A single adaptive controller is then associated with each actuator. This approach does not adequately address the dynamic nature of the cross-coupling.
The prior art fails to adequately address the dynamic cross-coupling in the vibrating device. Hence, cancellation of vibrations in complex systems cannot be achieved.